Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Count the degrees of freedom of one molecule of each gas. Then write as a multiple of . (a) Helium. (b) Carbon dioxide, a straight molecule, treated as rigid. (c) Steam, a bent molecule, treated as rigid. (d) Carbon monoxide so hot that its molecules vibrate.
Each squared term in the energy of a molecule has on average. Translation gives 3 terms, rotation 2 (linear) or 3 (bent), and each active vibration 2.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
(a) Helium. One atom, so it only moves: and .
(b) Carbon dioxide. It is straight, so it turns 2 ways: and .
(c) Steam. It is bent, so it turns 3 ways: and .
(d) Hot carbon monoxide. It moves 3 ways, turns 2 ways and vibrates. The vibration has 2 terms: and .
Watch out. A vibration is one motion, but it counts as two degrees of freedom.
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